| | step type | requirements | statement |
| 0 | modus ponens | 1, 2 | ⊢  |
| 1 | instantiation | 3, 4*, 5* | ⊢  |
| | : , : , :  |
| 2 | instantiation | 6, 7, 8 | ⊢  |
| | : , :  |
| 3 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.fold_forall_natural_pos |
| 4 | instantiation | 370, 9, 430 | ⊢  |
| | : , : , :  |
| 5 | instantiation | 10, 11 | ⊢  |
| | :  |
| 6 | theorem | | ⊢  |
| | proveit.logic.booleans.conjunction.and_if_both |
| 7 | instantiation | 432, 12, 13 | ⊢  |
| | : , : , :  |
| 8 | generalization | 14 | ⊢  |
| 9 | instantiation | 459, 423 | ⊢  |
| | : , : , :  |
| 10 | conjecture | | ⊢  |
| | proveit.physics.quantum.algebra.single_qubit_num_ket |
| 11 | instantiation | 15, 16, 17 | ⊢  |
| | :  |
| 12 | instantiation | 73, 558, 18, 19* | ⊢  |
| | :  |
| 13 | instantiation | 459, 20 | ⊢  |
| | : , : , :  |
| 14 | instantiation | 425, 21 | , ⊢  |
| | : , :  |
| 15 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.nonneg_int_is_natural |
| 16 | instantiation | 559, 22, 24 | ⊢  |
| | : , : , :  |
| 17 | instantiation | 23, 543, 537, 24 | ⊢  |
| | : , : , :  |
| 18 | instantiation | 401, 290, 25 | ⊢  |
| | : , : , :  |
| 19 | instantiation | 370, 26, 27 | ⊢  |
| | : , : , :  |
| 20 | instantiation | 28, 543, 537, 29, 30*, 31* | ⊢  |
| | : , : , : , :  |
| 21 | instantiation | 432, 32, 33 | , ⊢  |
| | : , : , :  |
| 22 | instantiation | 542, 543, 537 | ⊢  |
| | : , :  |
| 23 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.interval_lower_bound |
| 24 | assumption | | ⊢  |
| 25 | instantiation | 435, 456, 429 | ⊢  |
| | : , :  |
| 26 | instantiation | 459, 34 | ⊢  |
| | : , : , :  |
| 27 | instantiation | 35, 442, 36 | ⊢  |
| | : , : , :  |
| 28 | conjecture | | ⊢  |
| | proveit.linear_algebra.addition.vec_sum_split_first |
| 29 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.less_0_1 |
| 30 | instantiation | 370, 37, 38 | ⊢  |
| | : , : , :  |
| 31 | instantiation | 370, 39, 40 | ⊢  |
| | : , : , :  |
| 32 | instantiation | 401, 41, 42 | , ⊢  |
| | : , : , :  |
| 33 | instantiation | 43, 490, 44, 80, 45, 46, 47* | ⊢  |
| | : , : , : , :  |
| 34 | instantiation | 370, 48, 49 | ⊢  |
| | : , : , :  |
| 35 | axiom | | ⊢  |
| | proveit.linear_algebra.tensors.unary_tensor_prod_def |
| 36 | instantiation | 443, 442, 201, 50 | ⊢  |
| | : , : , : , :  |
| 37 | instantiation | 459, 51 | ⊢  |
| | : , : , :  |
| 38 | instantiation | 52, 456, 282, 442 | ⊢  |
| | : , : , :  |
| 39 | instantiation | 459, 317 | ⊢  |
| | : , : , :  |
| 40 | instantiation | 53, 537, 54* | ⊢  |
| | : , :  |
| 41 | instantiation | 401, 55, 56, 57* | , ⊢  |
| | : , : , :  |
| 42 | instantiation | 58, 353, 427, 546, 66, 479, 502, 503, 504, 505, 481 | ⊢  |
| | : , : , : , : , : , : , :  |
| 43 | conjecture | | ⊢  |
| | proveit.logic.equality.sub_in_right_operands_via_tuple |
| 44 | instantiation | 370, 59, 151 | ⊢  |
| | : , : , :  |
| 45 | instantiation | 73, 511, 60 | ⊢  |
| | :  |
| 46 | instantiation | 61, 62, 311* | ⊢  |
| | : , : , :  |
| 47 | modus ponens | 63, 64 | ⊢  |
| 48 | instantiation | 459, 65 | ⊢  |
| | : , : , :  |
| 49 | instantiation | 70, 353, 427, 66, 502, 503, 504, 505 | ⊢  |
| | : , : , : , :  |
| 50 | instantiation | 236, 442, 282, 67 | ⊢  |
| | : , : , : , :  |
| 51 | instantiation | 370, 68, 69 | ⊢  |
| | : , : , :  |
| 52 | conjecture | | ⊢  |
| | proveit.linear_algebra.scalar_multiplication.one_as_scalar_mult_id |
| 53 | axiom | | ⊢  |
| | proveit.linear_algebra.addition.vec_sum_single |
| 54 | instantiation | 70, 476, 546, 477, 479, 502, 503, 504, 505 | ⊢  |
| | : , : , : , :  |
| 55 | instantiation | 432, 71, 72 | , ⊢  |
| | : , : , :  |
| 56 | instantiation | 73, 561 | ⊢  |
| | :  |
| 57 | instantiation | 370, 74, 75 | ⊢  |
| | : , : , :  |
| 58 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.rightward_commutation |
| 59 | instantiation | 401, 76, 114 | ⊢  |
| | : , : , :  |
| 60 | instantiation | 370, 77, 78 | ⊢  |
| | : , : , :  |
| 61 | conjecture | | ⊢  |
| | proveit.core_expr_types.tuples.partition_front |
| 62 | instantiation | 432, 556, 79 | ⊢  |
| | : , : , :  |
| 63 | instantiation | 409, 201, 546, 556, 112, 479, 127 | ⊢  |
| | : , : , : , : , : , : , : , :  |
| 64 | instantiation | 437, 129, 175, 130, 442, 146, 80, 81, 128 | ⊢  |
| | : , : , : , :  |
| 65 | instantiation | 370, 82, 83 | ⊢  |
| | : , : , :  |
| 66 | instantiation | 385 | ⊢  |
| | : , : , :  |
| 67 | instantiation | 443, 442, 84, 439 | ⊢  |
| | : , : , : , :  |
| 68 | instantiation | 459, 85 | ⊢  |
| | : , : , :  |
| 69 | instantiation | 100, 86 | ⊢  |
| | :  |
| 70 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.elim_one_any |
| 71 | instantiation | 432, 87, 88 | ⊢  |
| | : , : , :  |
| 72 | assumption | | ⊢  |
| 73 | axiom | | ⊢  |
| | proveit.physics.quantum.QPE._psi_t_def |
| 74 | modus ponens | 89, 90 | ⊢  |
| 75 | modus ponens | 91, 92 | ⊢  |
| 76 | instantiation | 221, 93 | ⊢  |
| | : , : , :  |
| 77 | instantiation | 94, 546, 555, 427, 479, 420, 422, 456 | ⊢  |
| | : , : , : , : , : , :  |
| 78 | instantiation | 394, 456, 310 | ⊢  |
| | : , :  |
| 79 | instantiation | 370, 95, 96 | ⊢  |
| | : , : , :  |
| 80 | instantiation | 370, 97, 151 | ⊢  |
| | : , : , :  |
| 81 | instantiation | 443, 442, 201, 98 | ⊢  |
| | : , : , : , :  |
| 82 | instantiation | 459, 99 | ⊢  |
| | : , : , :  |
| 83 | instantiation | 100, 502 | ⊢  |
| | :  |
| 84 | instantiation | 559, 465, 101 | ⊢  |
| | : , : , :  |
| 85 | instantiation | 102, 476, 546, 477, 479, 502, 503, 504, 505 | ⊢  |
| | : , : , : , :  |
| 86 | instantiation | 559, 521, 103 | ⊢  |
| | : , : , :  |
| 87 | instantiation | 401, 104, 105 | ⊢  |
| | : , : , :  |
| 88 | modus ponens | 106, 107 | ⊢  |
| 89 | instantiation | 108, 427, 222, 546, 109, 240, 127, 479 | ⊢  |
| | : , : , : , : , : , : , : , :  |
| 90 | instantiation | 437, 538, 125, 442, 126, 110, 124, 111 | ⊢  |
| | : , : , : , :  |
| 91 | instantiation | 409, 201, 546, 556, 112, 479, 127 | ⊢  |
| | : , : , : , : , : , : , : , :  |
| 92 | instantiation | 437, 129, 175, 130, 442, 146, 113, 124, 128 | ⊢  |
| | : , : , : , :  |
| 93 | instantiation | 432, 490, 114 | ⊢  |
| | : , : , :  |
| 94 | conjecture | | ⊢  |
| | proveit.numbers.addition.subtraction.subtraction_disassociation |
| 95 | instantiation | 459, 311 | ⊢  |
| | : , : , :  |
| 96 | instantiation | 115, 422 | ⊢  |
| | :  |
| 97 | instantiation | 370, 116, 175 | ⊢  |
| | : , : , :  |
| 98 | instantiation | 236, 442, 282, 117 | ⊢  |
| | : , : , : , :  |
| 99 | conjecture | | ⊢  |
| | proveit.numbers.negation.negated_zero |
| 100 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.exp_zero_eq_one |
| 101 | instantiation | 482, 483, 118 | ⊢  |
| | : , :  |
| 102 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.mult_zero_any |
| 103 | instantiation | 559, 528, 516 | ⊢  |
| | : , : , :  |
| 104 | instantiation | 459, 119 | ⊢  |
| | : , : , :  |
| 105 | instantiation | 401, 120, 121 | ⊢  |
| | : , : , :  |
| 106 | instantiation | 409, 201, 546, 427, 410, 479, 122* | ⊢  |
| | : , : , : , : , : , : , : , :  |
| 107 | instantiation | 437, 538, 441, 442, 444, 123, 124, 220 | ⊢  |
| | : , : , : , :  |
| 108 | conjecture | | ⊢  |
| | proveit.linear_algebra.tensors.tensor_prod_disassociation |
| 109 | instantiation | 440, 538, 125, 442, 126 | ⊢  |
| | : , : , :  |
| 110 | instantiation | 495 | ⊢  |
| | : , :  |
| 111 | instantiation | 437, 144, 240, 145, 146, 127, 128 | ⊢  |
| | : , : , : , :  |
| 112 | instantiation | 440, 129, 175, 130, 442, 146 | ⊢  |
| | : , : , :  |
| 113 | instantiation | 370, 131, 151 | ⊢  |
| | : , : , :  |
| 114 | instantiation | 370, 132, 133 | ⊢  |
| | : , : , :  |
| 115 | conjecture | | ⊢  |
| | proveit.numbers.addition.elim_zero_left |
| 116 | instantiation | 203, 538, 134, 205, 206, 207, 222, 228*, 240* | ⊢  |
| | : , : , : , :  |
| 117 | instantiation | 443, 442, 135, 439 | ⊢  |
| | : , : , : , :  |
| 118 | instantiation | 499, 476, 477, 502, 503, 504, 505 | ⊢  |
| | : , :  |
| 119 | instantiation | 432, 136, 137 | ⊢  |
| | : , : , :  |
| 120 | instantiation | 432, 138, 139 | ⊢  |
| | : , : , :  |
| 121 | instantiation | 370, 140, 141 | ⊢  |
| | : , : , :  |
| 122 | instantiation | 370, 142, 143 | ⊢  |
| | : , : , :  |
| 123 | instantiation | 495 | ⊢  |
| | : , :  |
| 124 | instantiation | 443, 442, 201, 219 | ⊢  |
| | : , : , : , :  |
| 125 | instantiation | 495 | ⊢  |
| | : , :  |
| 126 | instantiation | 440, 144, 240, 145, 146 | ⊢  |
| | : , : , :  |
| 127 | instantiation | 370, 147, 168 | ⊢  |
| | : , : , :  |
| 128 | modus ponens | 148, 149 | ⊢  |
| 129 | instantiation | 526, 558, 561 | ⊢  |
| | : , :  |
| 130 | instantiation | 370, 150, 151 | ⊢  |
| | : , : , :  |
| 131 | instantiation | 370, 152, 175 | ⊢  |
| | : , : , :  |
| 132 | instantiation | 459, 311 | ⊢  |
| | : , : , :  |
| 133 | instantiation | 352, 546, 555, 479, 420, 422, 456 | ⊢  |
| | : , : , : , :  |
| 134 | instantiation | 495 | ⊢  |
| | : , :  |
| 135 | instantiation | 559, 465, 153 | ⊢  |
| | : , : , :  |
| 136 | instantiation | 432, 154, 155 | ⊢  |
| | : , : , :  |
| 137 | modus ponens | 156, 165 | ⊢  |
| 138 | instantiation | 459, 157 | ⊢  |
| | : , : , :  |
| 139 | instantiation | 461, 538, 158, 421, 159, 160 | ⊢  |
| | : , : , :  |
| 140 | instantiation | 459, 161 | ⊢  |
| | : , : , :  |
| 141 | instantiation | 425, 162 | ⊢  |
| | : , :  |
| 142 | instantiation | 459, 163 | ⊢  |
| | : , : , :  |
| 143 | instantiation | 164, 410, 165, 201, 238, 166* | ⊢  |
| | : , : , : , : , :  |
| 144 | instantiation | 432, 561, 240 | ⊢  |
| | : , : , :  |
| 145 | instantiation | 370, 167, 168 | ⊢  |
| | : , : , :  |
| 146 | instantiation | 169, 532, 543, 442, 172 | ⊢  |
| | : , : , :  |
| 147 | instantiation | 401, 170, 240 | ⊢  |
| | : , : , :  |
| 148 | instantiation | 171, 532, 543, 172 | ⊢  |
| | : , : , : , :  |
| 149 | generalization | 173 | ⊢  |
| 150 | instantiation | 370, 174, 175 | ⊢  |
| | : , : , :  |
| 151 | instantiation | 425, 176 | ⊢  |
| | : , :  |
| 152 | instantiation | 203, 538, 177, 205, 206, 207, 222, 228*, 240* | ⊢  |
| | : , : , : , :  |
| 153 | instantiation | 482, 483, 178 | ⊢  |
| | : , :  |
| 154 | instantiation | 432, 179, 180 | ⊢  |
| | : , : , :  |
| 155 | modus ponens | 181, 182 | ⊢  |
| 156 | instantiation | 183, 546, 555, 427, 410, 479, 184 | ⊢  |
| | : , : , : , : , : , : , : , :  |
| 157 | instantiation | 185, 538, 420, 422, 456, 502, 186 | ⊢  |
| | : , : , :  |
| 158 | instantiation | 495 | ⊢  |
| | : , :  |
| 159 | instantiation | 559, 521, 414 | ⊢  |
| | : , : , :  |
| 160 | instantiation | 559, 521, 187 | ⊢  |
| | : , : , :  |
| 161 | instantiation | 424, 188, 189 | ⊢  |
| | : , :  |
| 162 | instantiation | 190, 456, 191, 192, 193* | ⊢  |
| | : , : , : , :  |
| 163 | modus ponens | 194, 195 | ⊢  |
| 164 | conjecture | | ⊢  |
| | proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled |
| 165 | instantiation | 437, 538, 441, 442, 444, 196, 219, 239 | ⊢  |
| | : , : , : , :  |
| 166 | instantiation | 197, 201, 238 | ⊢  |
| | : , :  |
| 167 | instantiation | 401, 198, 240 | ⊢  |
| | : , : , :  |
| 168 | instantiation | 425, 199 | ⊢  |
| | : , :  |
| 169 | conjecture | | ⊢  |
| | proveit.logic.booleans.conjunction.redundant_conjunction_general |
| 170 | instantiation | 221, 222 | ⊢  |
| | : , : , :  |
| 171 | conjecture | | ⊢  |
| | proveit.logic.booleans.conjunction.conjunction_from_quantification |
| 172 | instantiation | 432, 200, 317 | ⊢  |
| | : , : , :  |
| 173 | instantiation | 443, 442, 201, 202 | , ⊢  |
| | : , : , : , :  |
| 174 | instantiation | 203, 538, 204, 205, 206, 207, 222, 228*, 240* | ⊢  |
| | : , : , : , :  |
| 175 | instantiation | 435, 456, 422 | ⊢  |
| | : , :  |
| 176 | instantiation | 223, 490 | ⊢  |
| | : , :  |
| 177 | instantiation | 495 | ⊢  |
| | : , :  |
| 178 | instantiation | 499, 500, 208, 502, 503, 504, 481, 505 | ⊢  |
| | : , :  |
| 179 | instantiation | 401, 209, 210 | ⊢  |
| | : , : , :  |
| 180 | modus ponens | 211, 212 | ⊢  |
| 181 | instantiation | 409, 406, 546, 427, 410, 479 | ⊢  |
| | : , : , : , : , : , : , : , :  |
| 182 | instantiation | 437, 538, 441, 442, 444, 213, 237, 239 | ⊢  |
| | : , : , : , :  |
| 183 | conjecture | | ⊢  |
| | proveit.linear_algebra.tensors.tensor_prod_distribution_over_add |
| 184 | instantiation | 495 | ⊢  |
| | : , :  |
| 185 | conjecture | | ⊢  |
| | proveit.numbers.division.distribute_frac_through_sum |
| 186 | instantiation | 214, 538 | ⊢  |
| | :  |
| 187 | instantiation | 559, 530, 215 | ⊢  |
| | : , : , :  |
| 188 | instantiation | 559, 521, 216 | ⊢  |
| | : , : , :  |
| 189 | instantiation | 559, 521, 217 | ⊢  |
| | : , : , :  |
| 190 | conjecture | | ⊢  |
| | proveit.numbers.division.prod_of_fracs |
| 191 | instantiation | 559, 497, 288 | ⊢  |
| | : , : , :  |
| 192 | instantiation | 559, 497, 348 | ⊢  |
| | : , : , :  |
| 193 | instantiation | 458, 456 | ⊢  |
| | :  |
| 194 | instantiation | 409, 238, 427, 546, 410, 479 | ⊢  |
| | : , : , : , : , : , : , : , :  |
| 195 | instantiation | 437, 538, 441, 442, 444, 218, 219, 220 | ⊢  |
| | : , : , : , :  |
| 196 | instantiation | 495 | ⊢  |
| | : , :  |
| 197 | axiom | | ⊢  |
| | proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult |
| 198 | instantiation | 221, 222 | ⊢  |
| | : , : , :  |
| 199 | instantiation | 223, 556 | ⊢  |
| | : , :  |
| 200 | instantiation | 224, 427, 546, 479, 225, 474 | ⊢  |
| | : , : , : , : , :  |
| 201 | instantiation | 559, 521, 226 | ⊢  |
| | : , : , :  |
| 202 | instantiation | 236, 442, 282, 227 | , ⊢  |
| | : , : , : , :  |
| 203 | conjecture | | ⊢  |
| | proveit.core_expr_types.tuples.general_len |
| 204 | instantiation | 495 | ⊢  |
| | : , :  |
| 205 | instantiation | 495 | ⊢  |
| | : , :  |
| 206 | instantiation | 495 | ⊢  |
| | : , :  |
| 207 | instantiation | 432, 427, 228 | ⊢  |
| | : , : , :  |
| 208 | instantiation | 517 | ⊢  |
| | : , : , : , : , :  |
| 209 | instantiation | 247, 229, 230 | ⊢  |
| | : , :  |
| 210 | instantiation | 370, 231, 232 | ⊢  |
| | : , : , :  |
| 211 | instantiation | 344, 427, 558, 546, 410, 479, 233* | ⊢  |
| | : , : , : , : , : , : , : , : , : , : , :  |
| 212 | generalization | 234 | ⊢  |
| 213 | instantiation | 495 | ⊢  |
| | : , :  |
| 214 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos |
| 215 | instantiation | 559, 468, 235 | ⊢  |
| | : , : , :  |
| 216 | instantiation | 559, 528, 383 | ⊢  |
| | : , : , :  |
| 217 | instantiation | 559, 528, 314 | ⊢  |
| | : , : , :  |
| 218 | instantiation | 495 | ⊢  |
| | : , :  |
| 219 | instantiation | 236, 442, 282, 237 | ⊢  |
| | : , : , : , :  |
| 220 | instantiation | 443, 444, 238, 239 | ⊢  |
| | : , : , : , :  |
| 221 | conjecture | | ⊢  |
| | proveit.core_expr_types.tuples.range_len |
| 222 | instantiation | 432, 556, 240 | ⊢  |
| | : , : , :  |
| 223 | conjecture | | ⊢  |
| | proveit.core_expr_types.tuples.range_from1_len |
| 224 | conjecture | | ⊢  |
| | proveit.numbers.addition.term_as_weak_upper_bound |
| 225 | instantiation | 559, 241, 242 | ⊢  |
| | : , : , :  |
| 226 | instantiation | 559, 528, 243 | ⊢  |
| | : , : , :  |
| 227 | instantiation | 443, 442, 244, 439 | , ⊢  |
| | : , : , : , :  |
| 228 | instantiation | 329, 546, 555, 427, 479, 245, 456, 429, 246* | ⊢  |
| | : , : , : , : , : , :  |
| 229 | instantiation | 247, 248, 249 | ⊢  |
| | : , :  |
| 230 | instantiation | 459, 250, 251*, 252* | ⊢  |
| | : , : , :  |
| 231 | instantiation | 370, 253, 254 | ⊢  |
| | : , : , :  |
| 232 | instantiation | 459, 255, 378* | ⊢  |
| | : , : , :  |
| 233 | modus ponens | 256, 257 | , ⊢  |
| 234 | instantiation | 443, 410, 445, 258 | , ⊢  |
| | : , : , : , :  |
| 235 | instantiation | 485, 346, 487 | ⊢  |
| | : , :  |
| 236 | conjecture | | ⊢  |
| | proveit.linear_algebra.addition.binary_closure |
| 237 | instantiation | 443, 442, 406, 439 | ⊢  |
| | : , : , : , :  |
| 238 | instantiation | 559, 521, 259 | ⊢  |
| | : , : , :  |
| 239 | modus ponens | 260, 261 | ⊢  |
| 240 | instantiation | 370, 262, 263 | ⊢  |
| | : , : , :  |
| 241 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_nonpos_within_real_nonpos |
| 242 | instantiation | 559, 264, 265 | ⊢  |
| | : , : , :  |
| 243 | instantiation | 306, 307, 314, 266 | ⊢  |
| | : , :  |
| 244 | instantiation | 559, 465, 267 | , ⊢  |
| | : , : , :  |
| 245 | instantiation | 495 | ⊢  |
| | : , :  |
| 246 | instantiation | 370, 268, 317 | ⊢  |
| | : , : , :  |
| 247 | theorem | | ⊢  |
| | proveit.logic.equality.rhs_via_equality |
| 248 | instantiation | 401, 269, 369, 270* | ⊢  |
| | : , : , :  |
| 249 | instantiation | 459, 271, 272*, 273* | ⊢  |
| | : , : , :  |
| 250 | modus ponens | 274, 275 | ⊢  |
| 251 | instantiation | 339, 540 | ⊢  |
| | : , :  |
| 252 | instantiation | 339, 540 | ⊢  |
| | : , :  |
| 253 | instantiation | 370, 276, 277 | ⊢  |
| | : , : , :  |
| 254 | instantiation | 425, 278 | ⊢  |
| | : , :  |
| 255 | instantiation | 425, 279 | ⊢  |
| | : , :  |
| 256 | instantiation | 409, 445, 427, 546, 410, 479 | , ⊢  |
| | : , : , : , : , : , : , : , :  |
| 257 | instantiation | 437, 538, 441, 442, 444, 280, 282, 412 | , ⊢  |
| | : , : , : , :  |
| 258 | instantiation | 437, 538, 441, 442, 444, 281, 282, 446 | , ⊢  |
| | : , : , : , :  |
| 259 | instantiation | 559, 528, 283 | ⊢  |
| | : , : , :  |
| 260 | instantiation | 379, 558, 444 | ⊢  |
| | : , : , : , : , : , :  |
| 261 | generalization | 412 | ⊢  |
| 262 | instantiation | 459, 284 | ⊢  |
| | : , : , :  |
| 263 | instantiation | 370, 285, 286 | ⊢  |
| | : , : , :  |
| 264 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.nonpos_int_within_rational_nonpos |
| 265 | instantiation | 559, 287, 541 | ⊢  |
| | : , : , :  |
| 266 | instantiation | 347, 288 | ⊢  |
| | :  |
| 267 | instantiation | 482, 483, 289 | , ⊢  |
| | : , :  |
| 268 | instantiation | 459, 290 | ⊢  |
| | : , : , :  |
| 269 | instantiation | 401, 291, 292 | ⊢  |
| | : , : , :  |
| 270 | instantiation | 370, 293, 294 | ⊢  |
| | : , : , :  |
| 271 | modus ponens | 295, 296 | ⊢  |
| 272 | instantiation | 339, 540 | ⊢  |
| | : , :  |
| 273 | instantiation | 339, 540 | ⊢  |
| | : , :  |
| 274 | instantiation | 376, 558 | ⊢  |
| | : , : , : , : , : , : , :  |
| 275 | generalization | 297 | ⊢  |
| 276 | instantiation | 459, 298, 299*, 301* | ⊢  |
| | : , : , :  |
| 277 | instantiation | 459, 300, 301*, 302* | ⊢  |
| | : , : , :  |
| 278 | modus ponens | 303, 304 | ⊢  |
| 279 | modus ponens | 305, 343 | ⊢  |
| 280 | instantiation | 495 | ⊢  |
| | : , :  |
| 281 | instantiation | 495 | ⊢  |
| | : , :  |
| 282 | conjecture | | ⊢  |
| | proveit.physics.quantum.algebra.ket_zero_in_qubit_space |
| 283 | instantiation | 306, 307, 383, 308 | ⊢  |
| | : , :  |
| 284 | instantiation | 309, 310, 456, 311* | ⊢  |
| | : , :  |
| 285 | instantiation | 370, 312, 313 | ⊢  |
| | : , : , :  |
| 286 | instantiation | 394, 456, 422 | ⊢  |
| | : , :  |
| 287 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.neg_int_within_nonpos_int |
| 288 | instantiation | 559, 515, 314 | ⊢  |
| | : , : , :  |
| 289 | instantiation | 499, 500, 315, 502, 503, 504, 316, 505 | , ⊢  |
| | : , :  |
| 290 | instantiation | 455, 351, 456, 317 | ⊢  |
| | : , : , :  |
| 291 | instantiation | 318, 543, 544, 323, 319, 320, 321* | ⊢  |
| | : , : , : , : , :  |
| 292 | instantiation | 322, 548, 323, 324, 325*, 326*, 327* | ⊢  |
| | : , : , : , : , :  |
| 293 | instantiation | 328, 427, 546, 479, 331, 429, 366 | ⊢  |
| | : , : , : , : , : , : , :  |
| 294 | instantiation | 329, 546, 555, 427, 479, 330, 331, 366, 429, 332* | ⊢  |
| | : , : , : , : , : , :  |
| 295 | instantiation | 376, 558 | ⊢  |
| | : , : , : , : , : , : , :  |
| 296 | generalization | 333 | ⊢  |
| 297 | instantiation | 334, 561, 540 | , ⊢  |
| | : , :  |
| 298 | modus ponens | 335, 336 | ⊢  |
| 299 | instantiation | 339, 540 | ⊢  |
| | : , :  |
| 300 | modus ponens | 337, 338 | ⊢  |
| 301 | instantiation | 339, 540 | ⊢  |
| | : , :  |
| 302 | instantiation | 339, 540 | ⊢  |
| | : , :  |
| 303 | instantiation | 340, 558, 410, 341 | ⊢  |
| | : , : , : , : , : , : , : , :  |
| 304 | modus ponens | 342, 343 | ⊢  |
| 305 | instantiation | 344, 427, 558, 546, 410, 479, 345* | ⊢  |
| | : , : , : , : , : , : , : , : , : , : , :  |
| 306 | conjecture | | ⊢  |
| | proveit.numbers.division.div_real_pos_closure |
| 307 | instantiation | 559, 450, 346 | ⊢  |
| | : , : , :  |
| 308 | instantiation | 347, 348 | ⊢  |
| | :  |
| 309 | conjecture | | ⊢  |
| | proveit.numbers.negation.distribute_neg_through_binary_sum |
| 310 | instantiation | 559, 521, 349 | ⊢  |
| | : , : , :  |
| 311 | instantiation | 367, 422 | ⊢  |
| | :  |
| 312 | instantiation | 392, 427, 555, 350, 351, 422, 429, 456 | ⊢  |
| | : , : , : , : , : , :  |
| 313 | instantiation | 352, 546, 353, 479, 354, 422, 429, 456 | ⊢  |
| | : , : , : , :  |
| 314 | instantiation | 355, 421 | ⊢  |
| | :  |
| 315 | instantiation | 517 | ⊢  |
| | : , : , : , : , :  |
| 316 | instantiation | 559, 521, 356 | , ⊢  |
| | : , : , :  |
| 317 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.add_0_1 |
| 318 | conjecture | | ⊢  |
| | proveit.linear_algebra.addition.vec_sum_split_after |
| 319 | instantiation | 357, 358 | ⊢  |
| | : , :  |
| 320 | instantiation | 359, 496, 396, 454, 360 | ⊢  |
| | : , : , :  |
| 321 | instantiation | 370, 361, 362 | ⊢  |
| | : , : , :  |
| 322 | conjecture | | ⊢  |
| | proveit.linear_algebra.addition.vec_sum_index_shift |
| 323 | instantiation | 547, 449, 549 | ⊢  |
| | : , :  |
| 324 | instantiation | 559, 552, 363 | ⊢  |
| | : , : , :  |
| 325 | instantiation | 364, 481 | ⊢  |
| | :  |
| 326 | instantiation | 392, 546, 555, 427, 479, 365, 368, 429, 366 | ⊢  |
| | : , : , : , : , : , :  |
| 327 | instantiation | 367, 481 | ⊢  |
| | :  |
| 328 | conjecture | | ⊢  |
| | proveit.numbers.addition.leftward_commutation |
| 329 | conjecture | | ⊢  |
| | proveit.numbers.addition.association |
| 330 | instantiation | 495 | ⊢  |
| | : , :  |
| 331 | instantiation | 401, 368, 369 | ⊢  |
| | : , : , :  |
| 332 | instantiation | 370, 371, 372 | ⊢  |
| | : , : , :  |
| 333 | instantiation | 401, 373, 374 | , ⊢  |
| | : , : , :  |
| 334 | conjecture | | ⊢  |
| | proveit.physics.quantum.algebra.prepend_num_ket_with_zero_ket |
| 335 | instantiation | 376, 558 | ⊢  |
| | : , : , : , : , : , : , :  |
| 336 | generalization | 375 | ⊢  |
| 337 | instantiation | 376, 558 | ⊢  |
| | : , : , : , : , : , : , :  |
| 338 | generalization | 377 | ⊢  |
| 339 | conjecture | | ⊢  |
| | proveit.core_expr_types.conditionals.satisfied_condition_reduction |
| 340 | conjecture | | ⊢  |
| | proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum_with_scalar_mult |
| 341 | instantiation | 432, 406, 378 | ⊢  |
| | : , : , :  |
| 342 | instantiation | 379, 558, 410 | ⊢  |
| | : , : , : , : , : , :  |
| 343 | generalization | 380 | ⊢  |
| 344 | conjecture | | ⊢  |
| | proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation_with_scalar_mult |
| 345 | modus ponens | 381, 382 | , ⊢  |
| 346 | instantiation | 559, 507, 558 | ⊢  |
| | : , : , :  |
| 347 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero |
| 348 | instantiation | 559, 515, 383 | ⊢  |
| | : , : , :  |
| 349 | instantiation | 473, 451 | ⊢  |
| | :  |
| 350 | instantiation | 495 | ⊢  |
| | : , :  |
| 351 | instantiation | 559, 521, 384 | ⊢  |
| | : , : , :  |
| 352 | conjecture | | ⊢  |
| | proveit.numbers.addition.elim_zero_any |
| 353 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.nat3 |
| 354 | instantiation | 385 | ⊢  |
| | : , : , :  |
| 355 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.sqrt_real_pos_closure |
| 356 | instantiation | 559, 530, 386 | , ⊢  |
| | : , : , :  |
| 357 | conjecture | | ⊢  |
| | proveit.numbers.addition.subtraction.nonneg_difference |
| 358 | instantiation | 387, 551 | ⊢  |
| | :  |
| 359 | conjecture | | ⊢  |
| | proveit.numbers.ordering.less_shift_add_right |
| 360 | instantiation | 388, 421, 389, 390, 391 | ⊢  |
| | : , : , :  |
| 361 | instantiation | 392, 546, 555, 427, 479, 393, 481, 429, 456 | ⊢  |
| | : , : , : , : , : , :  |
| 362 | instantiation | 394, 456, 481 | ⊢  |
| | : , :  |
| 363 | instantiation | 557, 551 | ⊢  |
| | :  |
| 364 | conjecture | | ⊢  |
| | proveit.numbers.addition.subtraction.add_cancel_basic |
| 365 | instantiation | 495 | ⊢  |
| | : , :  |
| 366 | instantiation | 559, 521, 395 | ⊢  |
| | : , : , :  |
| 367 | conjecture | | ⊢  |
| | proveit.numbers.negation.double_negation |
| 368 | instantiation | 559, 521, 396 | ⊢  |
| | : , : , :  |
| 369 | instantiation | 425, 397, 398* | ⊢  |
| | : , :  |
| 370 | axiom | | ⊢  |
| | proveit.logic.equality.equals_transitivity |
| 371 | instantiation | 459, 399 | ⊢  |
| | : , : , :  |
| 372 | instantiation | 425, 400 | ⊢  |
| | : , :  |
| 373 | instantiation | 401, 402, 403 | , ⊢  |
| | : , : , :  |
| 374 | instantiation | 404, 561, 540 | , ⊢  |
| | : , :  |
| 375 | instantiation | 424, 445, 406 | , ⊢  |
| | : , :  |
| 376 | conjecture | | ⊢  |
| | proveit.core_expr_types.lambda_maps.general_lambda_substitution |
| 377 | instantiation | 405, 546, 427, 479, 406, 445 | , ⊢  |
| | : , : , : , : , : , :  |
| 378 | instantiation | 407 | ⊢  |
| | :  |
| 379 | conjecture | | ⊢  |
| | proveit.linear_algebra.addition.summation_closure |
| 380 | instantiation | 443, 410, 445, 408 | , ⊢  |
| | : , : , : , :  |
| 381 | instantiation | 409, 445, 427, 546, 410, 479 | , ⊢  |
| | : , : , : , : , : , : , : , :  |
| 382 | instantiation | 437, 538, 441, 442, 444, 411, 439, 412 | , ⊢  |
| | : , : , : , :  |
| 383 | instantiation | 413, 421, 414 | ⊢  |
| | : , :  |
| 384 | instantiation | 559, 530, 415 | ⊢  |
| | : , : , :  |
| 385 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_3_typical_eq |
| 386 | instantiation | 559, 534, 416 | , ⊢  |
| | : , : , :  |
| 387 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound |
| 388 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.exponential_monotonocity |
| 389 | instantiation | 559, 450, 486 | ⊢  |
| | : , : , :  |
| 390 | instantiation | 559, 450, 417 | ⊢  |
| | : , : , :  |
| 391 | instantiation | 418, 451 | ⊢  |
| | :  |
| 392 | conjecture | | ⊢  |
| | proveit.numbers.addition.disassociation |
| 393 | instantiation | 495 | ⊢  |
| | : , :  |
| 394 | conjecture | | ⊢  |
| | proveit.numbers.addition.subtraction.add_cancel_triple_32 |
| 395 | instantiation | 473, 496 | ⊢  |
| | :  |
| 396 | instantiation | 559, 530, 419 | ⊢  |
| | : , : , :  |
| 397 | instantiation | 461, 538, 420, 421, 422, 456, 423* | ⊢  |
| | : , : , :  |
| 398 | instantiation | 424, 481, 502 | ⊢  |
| | : , :  |
| 399 | instantiation | 425, 426 | ⊢  |
| | : , :  |
| 400 | instantiation | 475, 546, 555, 427, 479, 428, 502, 429, 481, 430*, 431* | ⊢  |
| | : , : , : , : , : , :  |
| 401 | theorem | | ⊢  |
| | proveit.logic.equality.sub_right_side_into |
| 402 | instantiation | 432, 433, 434 | , ⊢  |
| | : , : , :  |
| 403 | instantiation | 435, 506, 481 | , ⊢  |
| | : , :  |
| 404 | conjecture | | ⊢  |
| | proveit.physics.quantum.algebra.prepend_num_ket_with_one_ket |
| 405 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.association |
| 406 | instantiation | 559, 465, 436 | ⊢  |
| | : , : , :  |
| 407 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.unary_mult_reduction |
| 408 | instantiation | 437, 538, 441, 442, 444, 438, 439, 446 | , ⊢  |
| | : , : , : , :  |
| 409 | conjecture | | ⊢  |
| | proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod |
| 410 | instantiation | 440, 538, 441, 442, 444 | ⊢  |
| | : , : , :  |
| 411 | instantiation | 495 | ⊢  |
| | : , :  |
| 412 | instantiation | 443, 444, 445, 446 | , ⊢  |
| | : , : , : , :  |
| 413 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.exp_real_pos_closure |
| 414 | instantiation | 559, 530, 447 | ⊢  |
| | : , : , :  |
| 415 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.zero_is_rational |
| 416 | instantiation | 559, 550, 448 | , ⊢  |
| | : , : , :  |
| 417 | instantiation | 559, 507, 511 | ⊢  |
| | : , : , :  |
| 418 | conjecture | | ⊢  |
| | proveit.numbers.ordering.less_than_successor |
| 419 | instantiation | 559, 534, 449 | ⊢  |
| | : , : , :  |
| 420 | instantiation | 495 | ⊢  |
| | : , :  |
| 421 | instantiation | 559, 450, 487 | ⊢  |
| | : , : , :  |
| 422 | instantiation | 559, 521, 451 | ⊢  |
| | : , : , :  |
| 423 | instantiation | 452, 502 | ⊢  |
| | :  |
| 424 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.commutation |
| 425 | theorem | | ⊢  |
| | proveit.logic.equality.equals_reversal |
| 426 | instantiation | 453, 481 | ⊢  |
| | :  |
| 427 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat1 |
| 428 | instantiation | 495 | ⊢  |
| | : , :  |
| 429 | instantiation | 559, 521, 454 | ⊢  |
| | : , : , :  |
| 430 | instantiation | 455, 456, 502, 457 | ⊢  |
| | : , : , :  |
| 431 | instantiation | 458, 481 | ⊢  |
| | :  |
| 432 | theorem | | ⊢  |
| | proveit.logic.equality.sub_left_side_into |
| 433 | instantiation | 459, 460 | , ⊢  |
| | : , : , :  |
| 434 | instantiation | 461, 538, 462, 516, 484, 463 | , ⊢  |
| | : , : , :  |
| 435 | conjecture | | ⊢  |
| | proveit.numbers.addition.commutation |
| 436 | instantiation | 482, 483, 463 | ⊢  |
| | : , :  |
| 437 | conjecture | | ⊢  |
| | proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space |
| 438 | instantiation | 495 | ⊢  |
| | : , :  |
| 439 | conjecture | | ⊢  |
| | proveit.physics.quantum.algebra.ket_one_in_qubit_space |
| 440 | conjecture | | ⊢  |
| | proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space |
| 441 | instantiation | 495 | ⊢  |
| | : , :  |
| 442 | instantiation | 464, 538 | ⊢  |
| | :  |
| 443 | conjecture | | ⊢  |
| | proveit.linear_algebra.scalar_multiplication.scalar_mult_closure |
| 444 | instantiation | 464, 551 | ⊢  |
| | :  |
| 445 | instantiation | 559, 465, 466 | , ⊢  |
| | : , : , :  |
| 446 | instantiation | 467, 561, 540 | , ⊢  |
| | : , :  |
| 447 | instantiation | 559, 468, 469 | ⊢  |
| | : , : , :  |
| 448 | instantiation | 554, 555, 470 | , ⊢  |
| | : , :  |
| 449 | instantiation | 559, 550, 471 | ⊢  |
| | : , : , :  |
| 450 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos |
| 451 | instantiation | 559, 530, 472 | ⊢  |
| | : , : , :  |
| 452 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.complex_x_to_first_power_is_x |
| 453 | conjecture | | ⊢  |
| | proveit.numbers.negation.mult_neg_one_left |
| 454 | instantiation | 473, 474 | ⊢  |
| | :  |
| 455 | conjecture | | ⊢  |
| | proveit.numbers.addition.subtraction.subtract_from_add |
| 456 | instantiation | 559, 521, 474 | ⊢  |
| | : , : , :  |
| 457 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.add_1_1 |
| 458 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.elim_one_left |
| 459 | axiom | | ⊢  |
| | proveit.logic.equality.substitution |
| 460 | instantiation | 475, 476, 555, 546, 477, 478, 479, 502, 503, 504, 505, 506, 481 | , ⊢  |
| | : , : , : , : , : , :  |
| 461 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.products_of_complex_powers |
| 462 | instantiation | 495 | ⊢  |
| | : , :  |
| 463 | instantiation | 499, 500, 480, 502, 503, 504, 505, 481 | ⊢  |
| | : , :  |
| 464 | conjecture | | ⊢  |
| | proveit.linear_algebra.complex_vec_set_is_vec_space |
| 465 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.complex_nonzero_within_complex |
| 466 | instantiation | 482, 483, 484 | , ⊢  |
| | : , :  |
| 467 | conjecture | | ⊢  |
| | proveit.physics.quantum.algebra.num_ket_in_register_space |
| 468 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational |
| 469 | instantiation | 485, 486, 487 | ⊢  |
| | : , :  |
| 470 | instantiation | 488, 489 | , ⊢  |
| | :  |
| 471 | instantiation | 554, 555, 490 | ⊢  |
| | : , :  |
| 472 | instantiation | 559, 534, 491 | ⊢  |
| | : , : , :  |
| 473 | conjecture | | ⊢  |
| | proveit.numbers.negation.real_closure |
| 474 | instantiation | 492, 493, 558 | ⊢  |
| | : , : , :  |
| 475 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.distribute_through_sum |
| 476 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.nat4 |
| 477 | instantiation | 494 | ⊢  |
| | : , : , : , :  |
| 478 | instantiation | 495 | ⊢  |
| | : , :  |
| 479 | conjecture | | ⊢  |
| | proveit.core_expr_types.tuples.tuple_len_0_typical_eq |
| 480 | instantiation | 517 | ⊢  |
| | : , : , : , : , :  |
| 481 | instantiation | 559, 521, 496 | ⊢  |
| | : , : , :  |
| 482 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.exp_complex_nonzero_closure |
| 483 | instantiation | 559, 497, 498 | ⊢  |
| | : , : , :  |
| 484 | instantiation | 499, 500, 501, 502, 503, 504, 505, 506 | , ⊢  |
| | : , :  |
| 485 | conjecture | | ⊢  |
| | proveit.numbers.division.div_rational_pos_closure |
| 486 | instantiation | 559, 507, 561 | ⊢  |
| | : , : , :  |
| 487 | instantiation | 559, 507, 538 | ⊢  |
| | : , : , :  |
| 488 | conjecture | | ⊢  |
| | proveit.numbers.negation.nat_closure |
| 489 | instantiation | 508, 509, 510 | , ⊢  |
| | :  |
| 490 | instantiation | 559, 560, 511 | ⊢  |
| | : , : , :  |
| 491 | instantiation | 559, 550, 561 | ⊢  |
| | : , : , :  |
| 492 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.unfold_subset_eq |
| 493 | instantiation | 512, 513 | ⊢  |
| | : , :  |
| 494 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_4_typical_eq |
| 495 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_2_typical_eq |
| 496 | instantiation | 559, 530, 514 | ⊢  |
| | : , : , :  |
| 497 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero |
| 498 | instantiation | 559, 515, 516 | ⊢  |
| | : , : , :  |
| 499 | conjecture | | ⊢  |
| | proveit.numbers.multiplication.mult_complex_closure |
| 500 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.nat5 |
| 501 | instantiation | 517 | ⊢  |
| | : , : , : , : , :  |
| 502 | instantiation | 559, 521, 518 | ⊢  |
| | : , : , :  |
| 503 | instantiation | 559, 521, 519 | ⊢  |
| | : , : , :  |
| 504 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.i_is_complex |
| 505 | instantiation | 559, 521, 520 | ⊢  |
| | : , : , :  |
| 506 | instantiation | 559, 521, 522 | , ⊢  |
| | : , : , :  |
| 507 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos |
| 508 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos |
| 509 | instantiation | 559, 523, 525 | , ⊢  |
| | : , : , :  |
| 510 | instantiation | 524, 532, 543, 525 | , ⊢  |
| | : , : , :  |
| 511 | instantiation | 526, 561, 558 | ⊢  |
| | : , :  |
| 512 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.relax_proper_subset |
| 513 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.nat_pos_within_real |
| 514 | instantiation | 559, 534, 548 | ⊢  |
| | : , : , :  |
| 515 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero |
| 516 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.e_is_real_pos |
| 517 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.tuple_len_5_typical_eq |
| 518 | instantiation | 559, 530, 527 | ⊢  |
| | : , : , :  |
| 519 | instantiation | 559, 528, 529 | ⊢  |
| | : , : , :  |
| 520 | conjecture | | ⊢  |
| | proveit.physics.quantum.QPE._phase_is_real |
| 521 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.complex_numbers.real_within_complex |
| 522 | instantiation | 559, 530, 531 | , ⊢  |
| | : , : , :  |
| 523 | instantiation | 542, 532, 543 | ⊢  |
| | : , :  |
| 524 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.interval_upper_bound |
| 525 | assumption | | ⊢  |
| 526 | conjecture | | ⊢  |
| | proveit.numbers.addition.add_nat_pos_closure_bin |
| 527 | instantiation | 559, 534, 533 | ⊢  |
| | : , : , :  |
| 528 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.real_pos_within_real |
| 529 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.pi_is_real_pos |
| 530 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.real_numbers.rational_within_real |
| 531 | instantiation | 559, 534, 535 | , ⊢  |
| | : , : , :  |
| 532 | instantiation | 547, 536, 537 | ⊢  |
| | : , :  |
| 533 | instantiation | 559, 550, 538 | ⊢  |
| | : , : , :  |
| 534 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.rational_numbers.int_within_rational |
| 535 | instantiation | 559, 539, 540 | , ⊢  |
| | : , : , :  |
| 536 | instantiation | 559, 552, 541 | ⊢  |
| | : , : , :  |
| 537 | instantiation | 559, 550, 558 | ⊢  |
| | : , : , :  |
| 538 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat2 |
| 539 | instantiation | 542, 543, 544 | ⊢  |
| | : , :  |
| 540 | assumption | | ⊢  |
| 541 | instantiation | 557, 561 | ⊢  |
| | :  |
| 542 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.int_interval_within_int |
| 543 | instantiation | 559, 545, 546 | ⊢  |
| | : , : , :  |
| 544 | instantiation | 547, 548, 549 | ⊢  |
| | : , :  |
| 545 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_within_int |
| 546 | axiom | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.zero_in_nats |
| 547 | conjecture | | ⊢  |
| | proveit.numbers.addition.add_int_closure_bin |
| 548 | instantiation | 559, 550, 551 | ⊢  |
| | : , : , :  |
| 549 | instantiation | 559, 552, 553 | ⊢  |
| | : , : , :  |
| 550 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.nat_pos_within_int |
| 551 | instantiation | 554, 555, 556 | ⊢  |
| | : , :  |
| 552 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.integers.neg_int_within_int |
| 553 | instantiation | 557, 558 | ⊢  |
| | :  |
| 554 | conjecture | | ⊢  |
| | proveit.numbers.exponentiation.exp_natpos_closure |
| 555 | theorem | | ⊢  |
| | proveit.numbers.numerals.decimals.nat2 |
| 556 | instantiation | 559, 560, 561 | ⊢  |
| | : , : , :  |
| 557 | conjecture | | ⊢  |
| | proveit.numbers.negation.int_neg_closure |
| 558 | conjecture | | ⊢  |
| | proveit.numbers.numerals.decimals.posnat1 |
| 559 | theorem | | ⊢  |
| | proveit.logic.sets.inclusion.superset_membership_from_proper_subset |
| 560 | conjecture | | ⊢  |
| | proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat |
| 561 | assumption | | ⊢  |
| *equality replacement requirements |